Electron beams used in instrumentation such as scanning electron microscopes, transmission electron microscopes, microprobes, etc. exhibit numerous deficiencies that limit the performance of these instruments. For example, electron beams are generally defined by apertures with hard edges, usually circular. Diffraction from these hard-edge apertures results in a beam profile known as an Airy disc, which can result in an undesirable point spread function (PSF) for the instrument. For applications where a tightly focused electron beam is used to form an image, it may be desirable to use a probe beam that has a different intensity profile, such as that described by a Gaussian distribution. In optical devices this is usually achieved using a Gaussian aperture. Such an aperture will not work for electron optical systems, however, due to incohorent scattering within the aperture material. In addition, electron beam optical systems typically exhibit aberrations that limit elecron beam focussing and imaging.